THE ECONOMICS OF HUMAN DEVELOPMENT

The Technology of Skill Formation

By Flavio Cunha and James Heckman*

It is well documented that people have diverse Greenwood, and Aranth Seshadri 2002; and abilities, that these abilities account for a sub- Roland Bénabou 2002). The implicit assump- stantial portion of the variation across people in tion in this approach is that inputs into the pro- socioeconomic success, and that persistent and duction of skills at different stages of childhood substantial ability gaps across children from var- are perfect substitutes. We argue that to account ious socioeconomic groups emerge before they for a large body of evidence, it is important to start school. The family plays a powerful role in build a model of skill formation with multiple shaping these abilities through genetics, parental stages of childhood, where inputs at different investments, and through choice of child envi- stages are complements, and where there is self ronments. From a variety of intervention studies, productivity of investment. In addition, in order it is known that ability gaps in children from dif- to rationalize the evidence, it is important to ferent socioeconomic groups can be reduced if recognize three distinct credit constraints oper- remediation is attempted at early ages. The reme- ating on the family and its children. First, the diation efforts that appear to be most effective inability of a child to choose its parents. This is are those that supplement family environments the fundamental constraint imposed by the acci- for disadvantaged children. Cunha et al. (2006), dent of birth. Second, the inability of parents to henceforth CHLM, present a comprehensive sur- borrow against their children’s future income to vey and discussion of this literature. finance investments in them. Third, the inability This paper uses a simple economic model of parents to borrow against their own income to of skill formation to organize this and other finance investments in their children. evidence summarized here and the findings This paper summarizes findings from the of related literatures in psychology, education, recent literature on child development and pres- and neuroscience. The existing economic mod- ents a model that explains them. A model that els of child development treat childhood as a is faithful to the evidence must recognize that single period (see, e.g., Gary S. Becker and (a) parental influences are key factors governing Nigel Tomes 1986; S. Rao Aiyagari, Jeremy child development; (b) early childhood invest- ments must be distinguished from late childhood * Cunha: Department of Economics, University of Chi­ investments; (c) an equity-efficiency trade-off cago, 1126 East 59th Street, Chicago, IL 60637 (e‑mail: ­[email protected]); Heckman: Department of Econom­ exists for late investments, but not for early ics, University of Chicago, 1126 East 59th Street, Chicago, investments; (d) abilities are created, not solely IL 60637 (e-mail: [email protected]). This research was inherited, and are multiple in variety; (e) the tra- supported by National Institutes of Health grant R01- ditional ability-skills dichotomy is misleading— HD043411, National Science Foundation grant SES- 024158, the Committee for Economic Development with a both skills and abilities are created; and (f) the grant from The Pew Charitable Trusts and the Partnership “nature versus nurture” distinction is obsolete. for America’s Economic Success, and the J.B. Pritzker Con­ These insights change the way we interpret evi- sortium on Early Childhood Development at the Harris dence and design policy about investing in chil- School of Public Policy of the University of Chicago. Cunha dren. Point (a) is emphasized in many papers. also acknowledges support from the Claudio Haddad dis- sertation fund at the University of Chicago. The views Point (b) is ignored in models that consider only expressed in this paper are those of the authors and not nec- one period of childhood investment. Points (c), essarily those of the funders listed here. The first draft of (d), and (e) have received scant attention in the this paper was presented at a conference at the Minneapolis formal literature on child investment. Point (f) is Federal Reserve in October 2003. We thank Gary S. Becker, Janet Currie, and Greg J. Duncan for helpful com- ignored in the literature that partitions the vari- ments. A Web site, http://jenni.uchicago.edu/tech-skill/, ance of child outcomes into components due to contains supporting material. nature and those due to nurture. 31 32 AEA PAPERS AND PROCEEDINGS MAY 2007

I. Observations about Human Diversity and Abilities are produced and gene expression is Human Development and governed by environmental conditions (Rutter Some Facts Our Model Explains 2006). Measured abilities are susceptible to environmental influences, including in utero Any analysis of human development must experiences, and also have genetic components. reckon with three empirically well-established These factors interact to produce behaviors and observations about ability. The first observa- abilities that have both a genetic and an acquired tion is that ability matters. A large number of character.,  Genes and environment cannot be empirical studies document that cognitive abil- parsed meaningfully by traditional linear mod- ity is a powerful determinant of wages, school- els that assign variance to each component. ing, participation in crime, and success in many Taking these observations as established, we aspects of social and economic life. The frenzy develop a simple economic model to explain the generated by Richard J. Herrnstein and Charles following six facts from the recent empirical A. Murray’s book The Bell Curve, because of literature. First, ability gaps between individu- its claims of genetic determinism, obscured its als and across socioeconomic groups open up real message, which is that cognitive ability is at early ages, for both cognitive and noncogni- an important predictor of socioeconomic suc- tive skills. See Figure 1 for a prototypical fig- cess (see, e.g., Heckman 1995; and Richard J. ure which graphs a cognitive test score by age Murnane, John B. Willett, and Frank Levy of child and socioeconomic status of the fam- 1995). ily. CHLM present many additional graphs of A second observation, more recently estab- child cognitive and noncognitive skills by age lished, is that abilities are multiple in nature. showing early divergence and then near paral- Noncognitive abilities (perseverance, motivation, lelism during school-going years across chil- time preference, risk aversion, self-esteem, self- dren with parents of different socioeconomic control, preference for leisure) have direct effects status. Levels of child skills are highly corre- on wages (controlling for schooling), schooling, lated with family background factors like paren- teen pregnancy, smoking, crime, performance tal education and maternal ability, which, when on achievement tests, and many other aspects statistically controlled for, largely eliminate of social and economic life. (Samuel Bowles, these gaps (see Pedro Carneiro and Heckman Herbert Gintis, and Melissa Osborne 2001; Lex 2003; CHLM, and our Web site). Experimental Borghans, Angela L. Duckworth, Heckman, and interventions with long-term follow-up confirm Bas ter Weel, forthcoming; and Heckman, Jora that changing the resources available to dis- Stixrud, and Sergio Urzua 2006). advantaged children improves their adult out- The third observation is that the nature ver- comes (see the studies surveyed in CHLM or sus nurture distinction is obsolete. The mod- David Blau and Janet Currie 2006.) Schooling ern literature on epigenetic expression teaches quality and school resources have relatively us that the sharp distinction between acquired small effects on ability deficits and have little skills and ability featured in the early human effect on test scores by age across children from capital literature is not tenable (see, e.g., Michael different socioeconomic groups, as displayed Rutter 2006 and Peter D. Gluckman and Mark in Figure 1 and related graphs (see Heckman, Hanson 2005). Additive “nature” and “nur- ture” models, while traditional and still used in many studies of heritability and family influ-  There is some evidence that gene expression affected ence, mischaracterize how ability is manifested. by environment is heritable (see Rutter 2006).  Some recent evidence on gene-environment interac- tions resulting from child maltreatment is presented in  For example, Becker (1993, 99–100) contrasts the Avshalom Caspi et al. (2002). Rutter (2006) surveys this implications for the earnings distribution of ability models evidence. of earnings and human capital models, claiming the latter  Permanent income is the measure of socioeconomic are more consistent with the empirical evidence on earn- status in this figure. See CHLM for the source of this figure ings. The implicit assumption in his analysis and the lit- and the precise definition of permanent income. erature it spawned is that ability is determined by “nature,”  These and other figures are posted at our Web site for i.e., is genetic, and outside the influence of family invest- this paper. See Figures D0–D8 on our Web site. ment strategies.  See Figures D1–D3 on our Web site. VOL. 97 NO. 2 The Technology of Skill Formation 33

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Figure 1. Children of the NLSY: Average Standardized Score for PIAT Math by Permanent Income Quartile

Source: Full sample of the Children of the National Longitudinal Survey of Youth. See our Web site for a full explanation of this figure.

Maria Isabel Larenas, and Urzua 2004; Stephen This is the region of the brain that governs emo- W. Raudenbush 2006). tion and self-regulation. Second, in both animal and human species, On average, the later remediation is given to there is compelling evidence of critical and sen- a disadvantaged child, the less effective it is. A sitive periods in the development of the child. study by Thomas G. O’Connor et al. (2000) of Some skills or traits are more readily acquired adopted Romanian infants reared in severely at certain stages of childhood than others (see deprived orphanage environments before being the evidence summarized in Eric I. Knudsen adopted supports this claim. The later the et al. 2006). For example, on average, if a sec- Romanian orphan was rescued from the social, ond language is learned before age 12, the child emotional and cognitive isolation of the orphan- speaks it without an accent (Elissa L. Newport age, the lower was his or her cognitive perfor- 1990). If syntax and grammar are not acquired mance at the age of six. Classroom remediation early on, they appear to be very difficult to learn programs designed to combat early cognitive later in life (Steven Pinker 1994). A child born deficits have a poor track record. with a cataract will be blind if the cataract is not At historically funded levels, public job train- removed within the first year of life. ing programs and adult literacy and educational Different types of abilities appear to be programs, like the GED, that attempt to remedi- manipulable at different ages. IQ scores become ate years of educational and emotional neglect stable by age 10 or so, suggesting a sensitive among disadvantaged individuals have a low period for their formation before age 10 (see economic return and produce meager effects Kenneth D. Hopkins and Glenn H. Brecht 1975). for most people. A substantial body of evidence There is evidence that adolescent interventions suggests that returns to adolescent education for can affect noncognitive skills (see CHLM). This the most disadvantaged and less able are lower evidence is supported by the neuroscience that than the returns for the more advantaged (Costas establishes the malleability of the prefrontal Meghir and Mårten Palme 2001; Carneiro and cortex into the early 20s (Ronald E. Dahl 2004). Heckman 2003 and the evidence they cite; and 34 AEA PAPERS AND PROCEEDINGS MAY 2007

Carneiro, Heckman, and Edward J. Vytlacil view. Holding ability fixed, minorities are more 2006). likely to attend college than others despite their The available evidence suggests that for many lower family incomes (see Stephen V. Cameron skills and abilities, later remediation for early dis- and Heckman 2001 and the references they cite). advantage to achieve a given level of adult perfor- Augmenting family income or reducing college mance may be possible but is much more costly tuition at the stage of the life cycle when a child than early remediation (Cunha and Heckman goes to college does not go far in compensating 2006). The economic returns to job training, for low levels of previous investment. high-school graduation, and college attendance Carneiro and Heckman present evidence that are lower for less able persons (see Carneiro and only a small fraction (at most 8 percent) of the Heckman 2003 and the studies they cite). families of adolescents in the United States are Third, despite the low returns to interventions credit constrained in making college participa- targeted toward disadvantaged adolescents, tion decisions. This evidence is supported by the empirical literature shows high economic Cameron and Christopher Taber (2004) and returns for remedial investments in young disad- Ralph Stinebrickner and Todd R. Stinebrickner vantaged children (see W. Steven Barnett 2004, (2006). Permanent family income plays an the evidence in CHLM, and the papers they cite). important role in explaining educational choices, This finding is a consequence of dynamic com- insofar as it is a proxy for the high level of plementarity and self-productivity captured by investment in abilities and skills that wealthier the technology developed in the next section. families provide, but it is not synonymous with Fourth, if early investment in disadvantaged family income in the adolescent years, or with children is not followed up by later investment, tuition and fees. its effect at later ages is lessened. Investments There is some evidence, however, that credit appear to be complementary and require follow- constraints operating in the early years have up to be effective. Currie and Duncan Thomas effects on adult ability and schooling outcomes (1995) document a decline in the performance (Greg J. Duncan and Jeanne Brooks-Gunn 1997; of Head Start (a national program that promotes Gordon B. Dahl and Lance J. Lochner 2005; school readiness) minority participants after Pamela Morris, Duncan, and Elizabeth Clark- they leave the program, return to disadvantaged Kaufmann 2005; and Duncan and Ariel Kalil environments, and receive the low levels of 2006). Carneiro and Heckman (2003) show investment experienced by many disadvantaged that controlling for family permanent income children (see our Web site, CHLM and Blau and reduces the estimated effect of early income on Currie 2006 for definitions of this and other early child outcomes. Permanent income has a strong intervention programs). effect on child outcomes. The strongest evidence Fifth, the effects of credit constraints on a for an effect of the timing of parental income child’s outcomes when the child reaches adult- for disadvantaged children is in their early hood depend on the age at which they bind for years. The best documented market failure in the child’s family. Recent research summa- the life cycle of skill formation in contemporary rized in Carneiro and Heckman (2002, 2003) American society is the inability of children to and in CHLM demonstrates the quantitative buy their parents or the lifetime resources that insignificance of family credit constraints in parents provide and not the inability of families the child’s college-going years in explaining a to secure loans for a child’s education when the child’s enrollment in college. Controlling for child is an adolescent. cognitive ability, under meritocratic policies Sixth, socioemotional (noncognitive) skills currently in place in American society, family foster cognitive skills and are an important income during the child’s college-going years product of successful families and success- plays only a minor role in determining child col- ful interventions in disadvantaged families. lege participation, although much public policy Emotionally nurturing environments produce is predicated on precisely the opposite point of more capable learners. The Perry Preschool Program, which was evaluated by random  Currie and Thomas (2000) present additional analyses assignment, did not boost participant adult IQ of the Head Start program. but enhanced performance of participants on VOL. 97 NO. 2 The Technology of Skill Formation 35 a number of dimensions, including scores on tant roles. For child investments, parents make achievement tests, employment, and reduced ­decisions and child opportunity costs are less participation in a variety of social pathologies relevant. The outputs at each stage in our tech- (see Lawrence J. Schweinhart et al. 2005 and the nology are the levels of each skill achieved at figures and tables on the Perry program posted that stage. Some stages of the technology may be at our Web site). more productive in producing some skills than other stages, and some inputs may be more pro- II. A Model of Skill Formation ductive at some stages than at other stages. The stages that are more effective in producing certain We now develop a model of skill formation skills are called “sensitive periods” for the ac- that can explain the six facts just presented, as quisition of those skills. If one stage alone is effec- well as additional findings from the literature on tive in producing a skill (or ability), it is called a child development. We use the terms “skill” and “critical period” for that skill. “ability” interchangeably. Both are produced by An important feature of our technology is environments, investment, and genes. that the skills produced at one stage augment Agents possess a vector of abilities at each the skills attained at later stages. This effect is age. These abilities (or skills) are multiple in termed self-productivity. It embodies the idea nature and range from pure cognitive abilities that skills acquired in one period persist into (e.g., IQ) to noncognitive abilities (patience, self future periods. It also embodies the idea that control, temperament, risk aversion, and time skills are self-reinforcing and cross fertilizing. preference). These abilities are used with differ- For example, emotional security fosters child ent weights in different tasks in the labor market exploration and more vigorous learning of cog- and in social life more generally. Achievement nitive skills. This has been found in animal spe- test scores, sometimes confused with IQ scores cies (Stephen J. Suomi 1999; Michael J. Meaney (e.g., Herrnstein and Murray 1994), are not pure 2001; and Judy Cameron 2004) and in humans measures of ability and are affected by cognitive, (Duncan et al. 2006; C. Cybele Raver, Pamela noncognitive, and environmental inputs (see, e.g., W. Garner, and Radiah Smith-Donald 2007, Karsten T. Hansen, Heckman, and Kathleen J. interpreting the ability of a child to pay atten- Mullen 2004; and Cunha and Heckman, 2007). tion as a socioemotional skill). A higher stock of The human skill formation process is gov- cognitive skills in one period raises the stock of erned by a multistage technology. Each stage cognitive skills in the next period. A second key corresponds to a period in the life cycle of a feature of skill formation is dynamic comple- child. While the child development literature mentarity. Skills produced at one stage raise the recognizes stages of development (see, e.g., productivity of investment at subsequent stages. Erik H. Erikson 1950), the economics of child In a multistage technology, complementarity development does not. Inputs or investments implies that levels of skill investments at differ- at each stage produce outputs at the next stage. ent ages bolster each other. They are synergistic. Like Yoram Ben-Porath (1967), we use a pro- Complementarity also implies that early invest- duction function to determine the relationship ment should be followed up by later investment between inputs and the output of skill. Unlike in order for the early investment to be produc- Ben-Porath, in our model, qualitatively different tive. Together, dynamic complementarity and inputs can be used at different stages, and the self-productivity produce multiplier effects technologies can be different at different stages which are the mechanisms through which skills of child development.10 beget skills and abilities beget abilities. Ben-Porath focuses on adult investments Dynamic complementarity, self-productivity where time and its opportunity cost play impor- of human capital, and multiplier effects imply an equity-efficiency trade-off for late child invest-  See the Figure D9 series. ments but not for early investments. These con-  CHLM briefly discuss the evidence on this point and cepts, embedded in alternative market settings, suggest a model of comparative advantage in occupational choice to supplement their model of skill formation. explain the six facts from the recent literature 10 We discuss the comparison between our technology summarized in the previous section. These fea- and that of Ben-Porath (1967) in Section B of our Web site. tures of the technology of skill formation have 36 AEA PAPERS AND PROCEEDINGS MAY 2007 consequences for the design and evaluation of for t 5 1, 2, … , T. We assume that ft is strictly public policies toward families. In particular, increasing and strictly concave in It , and twice con- they show why the returns to late childhood tinuously differentiable in all of its arguments.13 investment and remediation for young adoles- Technology (1) is written in recursive form. cents from disadvantaged backgrounds are so Substituting in (1) for ut, ut21, … , repeatedly, one low, while the returns to early investment in can rewrite the stock of skills at stage t 1 1, 14 children from disadvantaged environments are ut11, as a function of all past investments: so high. We now formalize these concepts in an over- (2) ut11 5 mt 1h, u1, I1, … , It 2, t 5 1, … , T. lapping generations model. An individual lives for 2T years. The first T years the individual is Dynamic complementarity arises when 2 a child of an adult parent. From age T 1 1 to 2T 0 ft (h ,ut, It)/0ut 0It9 . 0, i.e., when stocks of skills the individual lives as an adult and is the parent acquired by period t 2 1 (ut) make investment of a child. The individual dies at the end of the in period t (It) more productive. Such comple- period in which he is 2T years old, just before mentarity explains why returns to educational his child’s child is born. At every calendar year investments are higher at later stages of the there are an equal and large number of individu- child’s life cycle for more able children (those 11 als of every age t [ 51, 2, … , 2T 6. To simplify with higher ut). Students with greater early the notation, we do not explicitly subscript skills (cognitive and noncognitive) are more generations. efficient in later learning of both cognitive and A household consists of an adult parent and noncognitive skills. The evidence from the early his child. Parents invest in their children because intervention literature suggests that the enriched of altruism. They have common preferences and early preschool environments provided by the supply labor inelastically. Let It denote paren- Abecedarian, Perry, and CPC interventions pro- tal investments in child skill when the child is t mote greater efficiency in learning in school and years old, where t 5 1, 2, … , T. The output of the reduce problem behaviors (see Blau and Currie investment process is a skill vector. The parent 2006, CHLM, and our Web site for this evi- is assumed to fully control the investments in dence and descriptions of these early interven- the skills of the child, whereas in reality, as a tion programs). child matures, he gains much more control over Self-productivity arises when 0ft 1h, ut, It2/0ut . 0, the investment process.12 We ignore investments i.e., when higher stocks of skills in one period in the child’s adult years to focus on new ideas create higher stocks of skills in the next period. in this paper. We also keep government inputs For the case of skill vectors, this includes own (e.g., schooling) implicit. They can be modeled and cross effects. The joint effects of self-pro- as a component of It. ductivity and dynamic complementarity help We now describe how skills evolve over time. to explain the high productivity of investment Assume that each agent is born with initial con- in disadvantaged young children, and the lower ditions u1. Let h denote parental characteristics return to investment in disadvantaged adoles- (e.g., IQ, education, etc.). At each stage t, let ut cent children for whom the stock of skills is denote the vector of skill stocks. The technology low and hence the complementarity effect is of production of skill when the child is t years lower. These are facts two and three presented old is in Section I. This technology is sufficiently rich to describe (1) ut11 5 ft 1h, ut, It2, learning in rodents and macaque monkeys. More emotionally secure young animals explore their environments more actively and learn more quickly. This technology also explains the

11 We develop our formal overlapping generations (OLG) 13 These conditions are sufficient. There is no need for a model in Section C of our Web site. differentiability requirement for h, and the differentiability 12 A sketch of such a model is discussed in Carneiro, requirement with respect to ut can be weakened. Cunha, and Heckman (2003). 14 Examples are developed in Section A of our Web site. VOL. 97 NO. 2 The Technology of Skill Formation 37

evidence that the ability of the child to pay conditions and investments during childhood I1 attention affects subsequent academic achieve- and I2: ment. Cross-complementarity serves to explain fact six. This technology also captures the criti- (3) hr 5 m2 1h, u1, I1, I2 2. cal and sensitive periods in humans and animals documented by Knudsen et al (2006). We now The literature in economics assumes only define these concepts precisely. one period of childhood. It does not distinguish * Period t is a critical period for ut11 if between early investment and late investment. This produces the conventional specification which is a special case of technology (3), where 'u 1 'm 1h, u , I , . . ., I 2 t 1 5 t 1 1 t K 0 'Is 'Is (4) hr 5 m2 1h, u1, gI1 1 11 2 g2I2 2

* for all h, u1, I1, … , It , s Z t , and g 5 1/2. In this case, adult stocks of skills do not depend on how investments are distrib- uted over different periods of childhood. For 'ut11 'mt 1h, u1, I1, . . . , It 2 but 5 . 0 example, take two children, A and B, who have 'It* 'It* identical parents and the same initial condi-

tion u1, but have different investment profiles: for some h, u1, I1, … , It . child A receives no investment in period one and receives I units of investment in period two, A A This condition says that investments in ut11 I1 5 0, I2 5 I, while child B receives I units of are productive in period t* but not in any other investment in period one and zero units of invest- * * B B period s Z t . Period t is a sensitive period for ment in period two, I1 5 I, I2 5 0. According to 1 ut11 if (4), when g 5 /2, children A and B will have the same stocks of skills as adults. The timing of 'u t11 investment is irrelevant. Neither period one nor ` _ 'Is h 5 h, u1 5 u, I1 5 i1, . . . , It 5 it period two is critical. The polar opposite of perfect substitution is 'u t11 perfect complementarity: , ` _ * 'It h 5 h, u1 5 u, I1 5 i1, . . . , It 5 it . (5) hr 5 m2 1h, u1, min 5I1, I26 2. In words, period t* is a sensitive period rela- tive to period s if, at the same level of inputs, Technology (5) has the feature that adult stocks investment is more productive in stage t* than in of skills critically depend on how investments another stage s Z t*.15 are distributed over time. For example, if invest- Suppose for simplicity that T 5 2. In reality, ment in period one is zero, I1 5 0, then it does there are many stages in childhood, including not pay to invest in period two. If late investment 16 in utero experiences. Assume that u1, I1, I2 are is zero, I2 5 0, it does not pay to invest early. 17 scalars. The adult stock of skills, hr ( 5 u3), For the technology of skill formation defined by is a function of parental characteristics, initial (5), the best strategy is to distribute investments

evenly, so that I1 5 I2. Complementarity has a dual face. It is essential to invest early to get sat- isfactory adult outcomes. But it is also essential

15 to invest late to harvest the fruits of the early See CHLM for a definition of critical and sensitive 18 periods in terms of technology (1). These definitions are investment. Such dynamic complementarity developed further in Section B of our Web site. helps to explain the evidence by Currie and 16 Our technology applies to in utero and post-natal investments as well. See Jack P. Shonkoff and Deborah Phillips (2000) for evidence on the importance of such 18 Both periods are critical. Note that, in this case, the investments. production function is not strictly differentiable as required 17 CHLM analyze the vector case. See also the support- in our definition. Our definition can be extended to deal ing material on our Web site. with this limit case. 38 AEA PAPERS AND PROCEEDINGS MAY 2007

Thomas (1995) that for disadvantaged minority face of CES complementarity is that when f is students, early investments through Head Start small, high early investment should be followed have weak effects in later years if not followed with high late investment if the early investment up by later investments. This is fact four on our is to be harvested. In the extreme case when list. Our explanation is in sharp contrast to the f S 2`, (6) converges to (5). This technology one offered by Becker (1991) who explains weak explains facts two and three—why returns to Head Start effects by crowding out of parental education are low in the adolescent years for investment by public investment. That is a story disadvantaged (low h, low I1, low u2) adoles- of substitution against the child who receives cents but are high in the early years. Without investment in a one-period model of childhood. the proper foundation for learning (high levels 19 Ours is a story of dynamic complementarity. of u2) in technology (1), adolescent interventions A more general technology that captures have low returns. technologies (4) and (5) as special cases is a In a one-period model of childhood, inputs at standard CES: any stage of childhood are perfect substitutes. Application of the one-period model supports

f f 1/f (6) h9 5 m2Qh, u1, 3g1I1 2 1 11 2 g2 1I2 2 4 R the widely held but empirically unsupported intuition that diminishing returns make invest- for f # 1 and 0 # g # 1. The CES share param- ment in less advantaged adolescents more pro- eter g is a skill multiplier. It reveals the produc- ductive. As noted in fact two of Section I, the tivity of early investment not only in directly evidence suggests that just the opposite is true. boosting hr (through self-productivity), but also We next embed the technology in a market envi- in raising the productivity of I2 by increasing ronment with parental choice of inputs. u2 through first-period investments. Thus, I1 directly increases u2, which, in turn, affects the III. The Optimal Life-Cycle productivity of I2 in forming hr; g captures the Profile of Investments net effect of I1 on hr through both self-productiv- ity and direct complementarity.20 Using technology (6), we now show how the The elasticity of substitution 1/11 2 f2 is a ratio of early to late investments varies as a measure of how easy it is to substitute between function of f and g as a consequence of parental

I1 and I2. For a CES technology, f represents the choices in different market settings. Let w and r degree of complementarity (or substitutability) denote the wage and interest rates, respectively, between early and late investment in producing in a stationary environment. At the beginning of skills. The parameter f governs how easy it is adulthood, the parent draws the initial level of to compensate for low levels of stage 1 skills in skill of the child, u1, from the distribution J1u1 2. producing later skills. Upon reaching adulthood, the parent receives When f is small, low levels of early invest- bequest b. The state variables for the parent ment I1 are not easily remediated by later invest- are the parental skills, h, the parental financial ment I2 in producing human capital. The other resources, b, and the initial skill level of the child, u1. Let c1 and c2 denote the consumption of the household in the first and second period 19 We offer another explanation of the apparently weak Head Start effects below. of the life cycle of the child, respectively. The 20 ft Consider an example in which ft (h, ut, It) 5 [h1, t (ut) parent decides how to allocate the resources ft ft (rt/ft) 1 h2, t (It) 1 h3, t (h) ] for t 5 1, 2; r1 5 1, r2 , 1; among consumption and investments at differ- and h1, t 1 h2, t 1 h3, t 5 1. Then, substituting for u2, we ent periods, as well as bequests br, which may f1 f1 obtain m2(h, u1, I1, I2) 5 [h1, 2(h1, 1(u1) 1 h2, 1(I1) 1 f (f /f ) f f (r /f ) be positive or negative. Assuming that human h (h) 1) 2 1 1 h (I ) 2 1 h (h) 2] 2 2 . The parameter 3, 1 2, 2 2 3, 2 capital (parental and child) is scalar, the budget f2 describes how easy it is to compensate early neglect with second-period investment. The parameter f1 describes the constraint is compensation possibilities for overcoming adverse initial c2 1 I2 br conditions u1 with first-period investment. The technology (7) 1 1 1 c1 I1 2 in the text is obtained by setting f1 5 f2, h3, 1 5 h3, 2 5 11 1 r2 11 1 r2 h1, 1 5 0, so that g 5 h1 ,2 h2, 1 and h2, 2 5 1 2 g. See Sec­ tion A.1 on our Web site for further analysis of this and wh related cases. 5 wh 1 1 b. 11 1 r2 VOL. 97 NO. 2 The Technology of Skill Formation 39

Let b denote the utility discount factor and d ­different values of the complementarity param- denote the parental altruism toward the child. eter f, assuming r 5 0. When f S 2`, the Let u1 # 2 denote the utility function. The recur- ratio is not sensitive to variations in g. When sive formulation of the problem of the parent is f 5 0, the function (6) is

g 12g (8) 5 1 u 2 5 1 u 2 hr m2 h, 1,I1,I2 m2 h, 1, I 1 I2 .

V (h, b, u1) In this case, from equation (9), the optimal I1 /I2 is close to zero for low values of g, but explodes 2 22 5 max 5u 1c12 1 bu 1c22 1 b dE 3V1h9, b9, u91 246. to infinity as g approaches one. When CES complementarity is high, the skill The problem of the parent is to maximize (8) multiplier g plays a limited role in shaping the subject to (7) and technology (6).21 ratio of early to late investment. High early When f 5 1, so early and late investment are investment should be followed by high late perfect CES substitutes, the optimal investment investment. As the degree of CES complemen- strategy is straightforward. The price of early tarity decreases, the role of the skill multiplier investment is $1. The price of late investment increases, and the higher the multiplier, the is $1/11 1 r2. Thus, the parent can purchase more investment should be concentrated in the 11 1 r2 units of I2 for every unit of I1. The early ages. amount of human capital produced from one In a perfect credit market model, optimal unit of I1 is g, while $11 1 r2 of I2 produces investment levels are not affected by parental (1 1 r)(1 2 g) units of human capital. Thus, wages or endowments, or the parameters that two forces act in opposite directions. High pro- characterize the utility function u1 # 2.23 Note, ductivity of initial investment (the skill multi- however, that even in this “perfect” credit market plier g) drives the parent toward making early setting, parental investments depend on parental investments. The interest rate drives the par- skills, h, because these characteristics affect the ent to invest late. It is optimal to invest early if returns to investment. From the point of view g . 11 2 g2 11 1 r2. of the child, this is a market failure due to the As f S 2`, the CES production function accident of birth. Children would like to choose converges to the Leontief case and the optimal the optimal amount of parental characteristics h 24 investment strategy is to set I1 5 I2. In this case, to complement their initial endowment, u1. investment in the young is essential. At the same Consider the second credit constraint men- time, later investment is needed to harvest early tioned in the introduction, parental bequests investment. On efficiency grounds, early disad- must be nonnegative, i.e., parents cannot leave vantages should be perpetuated, and compensa- debts to their children. The problem of the par- tory investments at later ages are economically ent is to maximize (8) subject to (7), technology inefficient. (6), and the liquidity constraint For 2` , f , 1, the first-order conditions are necessary and sufficient given concavity of (10) br $ 0. the technology in terms of I1 and I2 . For an inte- rior solution, we can derive the optimal ratio of If constraint (10) binds, then early investment ^ early to late investment: under lifetime liquidity constraints, I1, is lower than the early investment under the perfect credit 1 market model, denoted *. The same is true for I g 1 2 f I1 (9) 1 5 c d . I 11 2 g2 11 1 r2 2 22 Table A1 on our Web site concisely summarizes this analysis. Figure 2 plots the ratio of early to late invest- 23 We refer to parental resources specific to a given ment as a function of the skill multiplier g under generation. 24 This thought experiment is whimsical. If parents cre- ate the child through genes and environment, the child is 21 Section C of our Web site develops this analysis for an not an independent actor. Under a homunculus theory, the overlapping-generations model. child would have an identity independent of the parent. 40 AEA PAPERS AND PROCEEDINGS MAY 2007

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^ * late investment, I2 , I2. Under this type of investment. This helps to explain fact five in market imperfection, underinvestment in skills Section I. starts at early ages and continues throughout The effects of government policies on promot- the life cycle of the child. This explains fact ing the accumulation of human capital depend one—that skill gaps open up early and are on the complementarity between early and late perpetuated.25 investment, as well as on whether the policies In this second case, both early and late invest- were anticipated by parents or not. For example, ment depend on parental initial wealth b for the the short-run effects of an unanticipated policy families for whom the liquidity constraint (10) that subsidizes late investment will have weaker binds. Children who come from constrained effects the greater the complementarity between families with lower b will have lower early and early and late investment. If the technology is late investment. Interventions that occur at early Leontief, there is no short-run impact of the stages would exhibit high returns, especially if policy on adolescent investment. At the time the they are followed up with resources to supple- policy is announced, poor parents have already ment late investment. Once the early stage made their early investment decisions and, in investment is realized, however, late remedia- the Leontief case, it is not possible to compen- tion for disadvantaged children would produce sate by increasing late investment as a response lower returns if early and late investment are to the subsidy. not perfect substitutes, and late investment is There is, however, a long-run effect of the more productive the higher the level of early policy. If the policy is a permanent change announced before the child is born, new par-

25 ents will adjust both early and late investment in Of course, other reasons why skill gaps open up response to the subsidy to late investment. Note early and are perpetuated are variation in h and u1, the parental environmental and initial endowment variables, that the same is true for an exogenous increase respectively. in the return to education. If there is strong VOL. 97 NO. 2 The Technology of Skill Formation 41 complementarity between early and late invest- from borrowing against their own future labor ment, in the short run we would expect weak income, which may affect their ability to finance reactions to the increase in returns to education investment in the child’s early years.26 This is as gauged by adolescent investment decisions the third constraint considered in the introduc- for the children from very poor family back- tion. To analyze this case, assume that parental grounds, but stronger reactions in the long run. productivity grows exogenously at rate a. Let This analysis provides an explanation for why s denote parental savings. We write the con- the college enrollment response to unanticipated straints facing the parent at each stage of the life increases in the returns to college were initially cycle of the child as: so strong for adolescents from advantaged ­families and initially so weak for adolescents (first stage) from less advantaged families. Adolescents from s less advantaged families are more likely to lack c1 1 I1 1 5 wh 1 b, the foundational skills that make college going 11 1 r2 ­productive, compared to adolescents from more advantaged families (see Figure D10 on our (second stage) Web site). br There is no trade-off between equity and effi- c2 1 I2 1 5 w11 1 a2h 1 s, ciency in early childhood investment. Govern­ 11 1 r2 ment policies to promote early accumulation of human capital should be targeted to the chil- where s $ 0 and br $ 0. The restriction s $ 0 dren of poor families. However, the optimal says that the parent cannot borrow income from second-period intervention for a child from a their old age to finance consumption and invest- disadvantaged environment depends critically ment when the child is in the first stage of the on the nature of technology (6). If I1 and I2 are life cycle. Some parents may be willing to do perfect CES complements, then a low level of I1 this, especially when a is high. In the case when cannot be compensated at any level of invest- s $ 0 and br $ 0 bind, and investments in dif- ment by a high I2. On the other hand, suppose ferent periods are not perfect substitutes, the that f 5 1, so the technology m2 can be writ- timing of income matters. To see this, note that s ten with inputs as perfect CES substitutes. In if u1c2 5 1c 2 12/s, the ratio of early to late this case, a second-period intervention can, in investment is principle, eliminate initial skill deficits (low values of ). At a sufficiently high level of sec- 1 I1 I g 1 2 f ond-period investment, it is technically possible 1 5 c d 2 g 1 to offset low first-period investment, but it may I2 11 2 11 r2 not be cost effective to do so. If g is sufficiently low relative to , it is more efficient to postpone 1 2 s r 1wh 1 b 2 I 2 1 2 f investment. 3 c 1 d . b 1 a 2 The concepts of critical and sensitive periods 1 11 2 wh I2 2 are defined in terms of the technical possibili- ties of remediation. Many noneconomists frame If early income is low with respect to late income, the question of remediation for adverse environ- the ratio I1/I2 will be lower than the optimal ments in terms of what is technically possible, ratio. The deviation from the optimal ratio will not what is economically efficient. Our analysis be larger the lower the elasticity of intertempo- considers both technological possibilities and ral substitution of consumption (captured by the costs. From an economic point of view, critical parameter s). Early income would not matter if and sensitive periods should be defined in terms s 5 1, which would be the case when consump- of the costs and returns of remediation, and not tion in stage one is a perfect substitute for con- solely in terms of technical possibilities. sumption in stage two. Substitutability through Another source of market failure arises when parents are subject to lifetime liquidity con- 26 This type of constraint is also analyzed by Elizabeth straints and constraints that prevent parents Caucutt and Lance J. Lochner (2004). 42 AEA PAPERS AND PROCEEDINGS MAY 2007 parental preferences can undo lack of substitut- Note that technology (11) allows for cross-pro- ability in the technology of skill formation. ductivity effects—cognitive skills may affect Our analysis of credit-constrained families, the accumulation of noncognitive skills and joined with a low value of f, interprets the evi- vice versa. They also allow for critical and sen- dence presented by Duncan and Brooks-Gunn sitive periods to differ by skill, as is required to (1997); Morris, Duncan, and Clark-Kaufmann account for fact two. (2005); Duncan and Kalil (2006); and Dahl and If cognitive and/or noncognitive skills deter- Lochner (2005) that the level of family income mine costs of effort, time preference, or risk in the early stages of childhood has some effect aversion parameters, parental investments affect on the level of ability and achievement of the child and adult behavior. Our analysis of pref- children. This is fact five of Section I. Our erence formation contrasts with the analyses of analysis also interprets the evidence of Carneiro Hideo Akabayashi (1996) and Bruce A. Wein­ and Heckman (2002) and Cameron and Taber berg (2001). Those authors build principal-agent (2004) that, conditioning on child ability, family models where the parent (the principal) and the income in the adolescent years has only a minor child (the agent) agree on contracts in which effect on adolescent schooling choices. parents’ financial transfers are conditional on observable measures of effort (e.g., test scores IV. Cognitive and Noncognitive in school). These contracts are designed so that Skill Formation the children are driven toward the level of effort desired by the parents. In our model, parents A large body of research documents the directly shape child preferences. socioemotional basis of reason (see Antonio R. Accounting for preference formation enables us Damasio 1994; Joseph E. LeDoux 1996). Our to interpret the success of many early childhood analysis goes beyond this literature to formal- programs targeted to disadvantaged children that ize a body of evidence that emotional skills do not permanently raise IQ, but permanently promote learning. Mechanisms relating cortisol boost social performance.28 This is fact six of to stress and the effects of cortisol on the brain Section I. The controversy over Head Start fade- development of animals have been documented out may have been a consequence of relying only by Suomi (1999) and Meaney (2001). Duncan et on cognitive measures to gauge performance. al. (2006) and Raver, Garner, and Smith-Donald The Perry Preschool Program had an IQ fadeout (2007) show that a child’s ability to pay atten- but a lasting effect on a variety of participants tion facilitates later learning. through age 40. They work harder, are less likely The framework developed in Section II read- to commit crime, and participate in fewer social ily accommodates skill vectors.27 The evidence pathologies than do control group members.29 summarized in Section I shows the importance of both cognitive and noncognitive skills in deter- V. Estimates of the Technology mining adult outcomes. Child development is not just about cognitive skill formation, although Cunha and Heckman (2007) and Cunha, a lot of public policy analysis focuses solely on Heckman, and Schennach (2007) estimate cognitive test scores. Let ut denote the vector of recursive multistage technology (6) with cogni- C N cognitive and noncognitive skills: ut 5 1ut ,ut 2. tive and noncognitive skills generating adult out­ Let It denote the vector of investment in cog- comes like schooling, earnings, and occupational C N nitive and noncognitive skills: It 5 1It ,It 2. We use h 5 1hC,hN 2 to denote parental cognitive and noncognitive skills. At each stage , we can t 28 The Abecedarian early intervention program perma- define a recursive technology for cognitive skills nently boosted adult IQ (see CHLM). 1k 5 C2, and noncognitive skills, 1k 5 N2: 29 See the D9 series on our Web site. The exact mecha- nism by which noncognitive skills are boosted is not yet k k C N k C N established. It could be that noncognitive skills are created (11) u 5 1u u 2 [ 5 6 t11 f t t , t , I t ,h,h , k C,N . directly in the early years and persist. It could also be that the higher early cognitive skills that fade out foster noncog- nitive skills that persist. Both channels of influence could 27 See Section B on our Web site. be in operation. VOL. 97 NO. 2 The Technology of Skill Formation 43 choice.30 They develop new econometric meth- by Cunha, Heckman, and Schennach (2007) ods that extend factor analysis to a nonlinear to show the importance of self-productivity setting. We refer the reader to those papers for and complementarity for designing policies econometric details and discussions of the rich to reduce inequality. We focus our analysis panel data on child development that makes on children from disadvantaged backgrounds such estimation possible. because at current levels of social inequality They find strong evidence of self-productivity they benefit the most from policies that supple- and complementarity. Their evidence is consis- ment early environments.31 Disadvantaged chil- tent with the literature demonstrating malleabil- dren are at risk of being permanently poor and ity of the prefrontal cortex governing executive uneducated, and of participating in crime. In our function and socioeconomic development, as simulation, disadvantaged children come from a well as the stability of IQ measures after age background where mothers are in the first (low- 10 cited in Section I. They find higher substitut- est) decile in the distribution of parental skills. ability of early and late investment in producing If no intervention occurs, the children receive noncognitive skills and lower substitutability of investments equivalent to the first decile of the early investment in producing cognitive skills. distribution of parental investments. Higher stocks of noncognitive skills promote Consider three different policies. The first the self-productivity of cognitive skills; cogni- policy is a Perry Preschool–like policy. It pro- tive skill stocks promote the self-productivity of vides investment at early ages that moves chil- noncognitive skills. Higher levels of both cogni- dren from the first decile of child cognitive skills tive and noncognitive skills raise the productiv- at entry age to the fourth decile of child skills ity of subsequent investment. There is evidence at the age of exit from the program. This gain of sensitive periods for parental investment. The can be achieved by moving parental investment productivity of parental investment is higher in from the bottom decile to around the seventh early stages for cognitive skills with a fall off in decile of the family investment distribution. In their productivity in later years. The productiv- this policy, there is no follow-up investment. We ity of parental investment is higher at later stages also consider a second policy for the same tar- for noncognitive skills. This evidence is consis- get population that postpones remediation until tent with greater malleability of the prefrontal adolescence. It compensates early shortfalls by cortex governing socioemotional development investing larger amounts in adolescent stages of into the early 20s, documented by Dahl (2004). the life cycle to produce approximately the same Cunha, Heckman, and Schennach (2007) esti- high-school graduation rates that are observed mate a strong interaction between initial endow- in the Perry program. ments and parental investments that calls into College tuition programs, adolescent literacy question the conventional additive model of programs, and mentoring programs are exam- nature versus nurture. This evidence is consis- ples of such a policy. To achieve Perry-like out- tent with the modern literature on epigenetics. comes for this population through adolescent Nature and nurture interact to produce child investment, it is necessary to move adolescent outcomes and environmental effects that last investment to the ninth decile of the parental across generations. Even u1, endowment at investment distribution. The present value of birth, is affected by environmental factors as a the costs of the investment in this adolescent large literature documents (see, e.g., Shonkoff remediation program is more than 35 percent and Phillips 2000). larger than in the Perry Preschool program. Late remediation is possible, but it is costly. The case VI. Lessons for the Design of Policies for early childhood intervention is based more on the importance of sensitive periods in the Cunha and Heckman (2006) simulate the life cycle of the child than on the importance nonlinear model of skill formation estimated of critical periods. We contrast early-only and late-only investment policies with a third policy 30 Anchoring test score outcomes in behavior avoids reli- that optimally distributes the resources spent ance on arbitrarily scaled test scores as a measure of output (see Cunha and Heckman 2007 and Cunha et al. 2007). 31 This is fact three of Section I. 44 AEA PAPERS AND PROCEEDINGS MAY 2007

Table 1—Comparison of Different Investment Strategies (Disadvantaged children: First decile in the distribution of cognitive and noncognitive skills at age 6; mothers are in first decile in the distribution of cognitive and noncognitive skills at ages 14–21)

Changing initial conditions: Moving chil- Adolescent intervention: dren to the 4th decile of Moving investments Changing initial distribution of skills only at last transition from conditions and performing Baseline through early investment 1st to 9th decile a balanced intervention High-school graduation 0.4109 0.6579 0.6391 0.9135 Enrollment in college 0.0448 0.1264 0.1165 0.3755 Conviction 0.2276 0.1710 0.1773 0.1083 Probation 0.2152 0.1487 0.1562 0.0815 Welfare 0.1767 0.0905 0.0968 0.0259 Note: The adolescent-only and balanced intervention programs cost 35 percent more than the Perry program. Source: Cunha and Heckman (2006).

in the second policy over the full life cycle of those obtained in the Perry-like intervention. the child. A balanced investment strategy is the Adolescent interventions can be effective, but most efficient. they are more costly than early interventions. The first column of numbers in Table 1 reports The greater cost associated with later remedia- high-school graduation, college enrollment, tion arises from lost gains in self-productivity conviction, probation, and use of welfare if no and dynamic complementarity from early invest- intervention is made. Our model predicts a 41 ment that are key features of our model. percent high-school graduation rate for this The empirical importance of dynamic com- group, compared to 41.4 percent found in the plementarity—the fact that the marginal produc- Perry control group. Only 4.5 percent of the tivity of investment depends on the level of skills control group ever enrolls in college. Around produced by previous investments—generates 22 percent of them will be convicted of a crime an important insight for the design of policies. or be on probation at some point in their adult For a fixed expenditure, policies that are bal- lives. About 18 percent will make use of welfare anced increase returns and are more productive programs in their adult years. than policies tailored to one segment of the life The second column in Table 1 reports the cycle of the child. The returns to later investment performance of our Perry-like early interven- are greater if higher early investment is made. tion policy. This policy increases high-school Perry children made less use of remedial edu- graduation and college enrollment rates to more cation than peers who did not receive treatment. than 65 percent and 12 percent, respectively. The intervention made later schooling more It reduces participation in crime. It makes the effective. If early interventions are followed up children more productive when they are adults. with later interventions in an optimal fashion, It cuts in half the probability that the child col- outcomes can be considerably improved. lects welfare benefits in his/her early adult years. The fourth column in Table 1 presents the These effects are comparable to those reported results from a balanced policy. It displays the in the Perry preschool intervention (see, e.g., outcomes that can be produced by an inter- Schweinhart et al. 2005). Thus, with our tech- vention that distributes the funds spent on the nology, we can rationalize the results found in ­adolescent-only intervention in an optimal way. the Perry program as an intervention that boosts For a balanced program, high-school graduation parental investments (but not parental charac- and college enrollment rates are 91 percent and teristics) from the first decile of investment in 37 percent, respectively. The reduction in con- children to the fourth decile. viction and probation rates is better than what The third column in Table 1 displays the per- is obtained from an adolescent-only policy, formance of a 35 percent more costly policy that and welfare use is reduced to a low rate of 2.6 produces comparable educational outcomes for percent. Complementarity implies that early VOL. 97 NO. 2 The Technology of Skill Formation 45 investment is more productive if it is followed Barker, David J. P. 1998. Mothers, Babies and up with late investment. And late investment is Health in Later Life. Edinburgh: Churchill more productive if it is preceded by early invest- Livingstone. ment. The mechanism that makes the balanced Barnett, W. Steven. 2004. “Benefit-Cost Analy­ intervention more effective has a very simple sis of Preschool Education.” http://nieer.org/ economic interpretation. When adolescent-only resources/files/BarnettBenefits.ppt. interventions are made, baseline skills are low Becker, Gary S. 1991. A Treatise on the Family. and, consequently, so is the marginal productiv- Cambridge, MA: Harvard University Press. ity of later investment. A balanced investment Becker, Gary S. 1993. Human Capital: A Theo­ program increases the stock of skills of the child retical and Empirical Analysis, with Special coming into adolescence. Because the marginal Reference to Education. 3rd ed. Chicago: Uni­ productivity of later investment depends on the versity of Chicago Press. level of skills acquired prior to adolescence, the Becker, Gary S., and Nigel Tomes. 1986. “Human investment in the last period is more productive. 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